Stixrude receives James B. Macelwane Medal

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95034/1/eost12216.pd

Thermodynamics of mantle minerals – I. Physical properties

We present a theory for the computation of phase equilibria and physical properties of multicomponent assemblages relevant to the mantle of the Earth. The theory differs from previous treatments in being thermodynamically self-consistent: the theory is based on the concept of fundamental thermodynamic relations appropriately generalized to anisotropic strain and in encompassing elasticity in addition to the usual isotropic thermodynamic properties. In this first paper, we present the development of the theory, discuss its scope, and focus on its application to physical properties of mantle phases at elevated pressure and temperature including the equation of state, thermochemical properties and the elastic wave velocities. We find that the Eulerian finite strain formulation captures the variation of the elastic moduli with compression. The variation of the vibrational frequencies with compression is also cast as a Taylor series expansion in the Eulerian finite strain, the appropriate volume derivative of which leads to an expression for the GrÜneisen parameter that agrees well with results from first principles theory. For isotropic materials, the theory contains nine material-specific parameters: the values at ambient conditions of the Helmholtz free energy, volume, bulk and shear moduli, their pressure derivatives, an effective Debye temperature, its first and second logarithmic volume derivatives (Γ 0 , q 0 ) , and the shear strain derivative of Γ. We present and discuss in some detail the results of a global inversion of a wide variety of experimental data and first principles theoretical results, supplemented by systematic relations, for the values of these parameters for 31 mantle species. Among our findings is that the value of q is likely to be significantly greater than unity for most mantle species. We apply the theory to the computation of the shear wave velocity, and temperature and compositional (Fe content) derivatives at relevant mantle pressure temperature conditions. Among the patterns that emerge is that garnet is anomalous in being remarkably insensitive to iron content or temperature as compared with other mantle phases.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73485/1/j.1365-246X.2005.02642.x.pd

Self-consistent thermodynamic description of silicate liquids, with application to shock melting of MgO periclase and MgSiO 3 perovskite

We develop a self-consistent thermodynamic description of silicate liquids applicable across the entire mantle pressure and temperature regime. The description combines the finite strain free energy expansion with an account of the temperature dependence of liquid properties into a single fundamental relation, while honouring the expected limiting behaviour at large volume and high temperature. We find that the fundamental relation describes well previous experimental and theoretical results for liquid MgO, MgSiO 3 , Mg 2 SiO 4 and SiO 2 . We apply the description to calculate melting curves and Hugoniots of solid and liquid MgO and MgSiO 3 . For periclase, we find a melting temperature at the core–mantle boundary (CMB) of 7810 ± 160 K , with the solid Hugoniot crossing the melting curve at 375 GPa, 9580 K , and the liquid Hugoniot crossing at 470 GPa, 9870 K . For complete shock melting of periclase we predict a density increase of 0.14 g cm −3 and a sound speed decrease of 2.2 km s −1 . For perovskite, we find a melting temperature at the CMB of 5100 ± 100 K with the perovskite section of the enstatite Hugoniot crossing the melting curve at 150 GPa, 5190 K , and the liquid Hugoniot crossing at 220 GPa, 5520 K . For complete shock melting of perovskite along the enstatite principal Hugoniot, we predict a density increase of 0.10 g cm −3 , with a sound speed decrease of 2.6 km s −1 .Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75103/1/j.1365-246X.2009.04142.x.pd

Inferring the thermochemical structure of the upper mantle from seismic data

We test a mineral physics model of the upper mantle against seismic observations. The model is based on current knowledge of material properties at high temperatures and pressures. In particular, elastic properties are computed with a recent self-consistent thermodynamic model, based on a six oxides (NCFMAS) system. We focus on average structure between 250 and 800 km. We invert normal modes eigenfrequencies and traveltimes to obtain best-fitting average thermal structures for various compositional profiles. The thermochemical structures are then used to predict long-period waveforms, SS precursors waveforms and radial profiles of attenuation. These examples show the potential of our procedure to refine the interpretation combining different data sets.We found that a mixture of MORB and Harzburgite, with the MORB component increasing with depth, is able to reproduce well all the seismic data for realistic thermal structures. If the proportions of MORB with depth do not change, unrealistic negative thermal gradients below 250 km would be necessary to explain the data. Equilibrium assemblages, such as pyrolite, cannot fit the seismic data.The elastic velocities predicted by the reference mineral physics model tested are too low at the top of the lower mantle, even for the fastest (and most depleted) composition, that is, harzburgite. An increase in V P of 1 per cent and in V S of 2 per cent improves the data fit significantly and is required to find models that fit both traveltimes and normal modes, indicating the need for further experimental measurements of these properties at the simultaneously elevated pressure–temperature conditions of the lower mantle.Extending our procedure to other seismic and density data and interpreting the 3-D structure holds promise to further improve our knowledge of the thermochemical structure of the upper mantle. In addition, the same database of material properties can be used in dynamic models to test whether the thermochemical structure inferred from geophysical observations is consistent with the Earth's evolution.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78699/1/j.1365-246X.2009.04338.x.pd

Inferring the thermochemical structure of the upper mantle from seismic data

We test a mineral physics model of the upper mantle against seismic observations. The model is based on current knowledge of material properties at high temperatures and pressures. In particular, elastic properties are computed with a recent self-consistent thermodynamic model, based on a six oxides (NCFMAS) system. We focus on average structure between 250 and 800 km. We invert normal modes eigenfrequencies and traveltimes to obtain best-fitting average thermal structures for various compositional profiles. The thermochemical structures are then used to predict long-period waveforms, SS precursors waveforms and radial profiles of attenuation. These examples show the potential of our procedure to refine the interpretation combining different data sets. We found that a mixture of MORB and Harzburgite, with the MORB component increasing with depth, is able to reproduce well all the seismic data for realistic thermal structures. If the proportions of MORB with depth do not change, unrealistic negative thermal gradients below 250 km would be necessary to explain the data. Equilibrium assemblages, such as pyrolite, cannot fit the seismic data. The elastic velocities predicted by the reference mineral physics model tested are too low at the top of the lower mantle, even for the fastest (and most depleted) composition, that is, harzburgite. An increase in VP of 1 per cent and in VS of 2 per cent improves the data fit significantly and is required to find models that fit both traveltimes and normal modes, indicating the need for further experimental measurements of these properties at the simultaneously elevated pressure—temperature conditions of the lower mantle. Extending our procedure to other seismic and density data and interpreting the 3-D structure holds promise to further improve our knowledge of the thermochemical structure of the upper mantle. In addition, the same database of material properties can be used in dynamic models to test whether the thermochemical structure inferred from geophysical observations is consistent with the Earth's evolutio